You log on to the Browser Console through the Console object and publish as a property on SYS_WEB. You can easily log messages and information to the console using code like this:
#sys_web.Console.Log( #Message )
This results in the details being logged to the console when they are executed. To activate the Browser Console use F12 when in the browser and select Console in the menu.
For more information on the Browser Developer Tools (including the Console) refer to Browser Developer Tools - A Web Developer's Best Friend.